Decoupling synchrophasor based control system for multiple distributed energy resources

ABSTRACT

A method and system to control distributed energy resources in an electric power system includes generation, storage and controllable loads. The system uses time synchronized measurements of voltage phasor and current phasors and their derivative information that may include real and reactive power to regulate and decouple both static and dynamic effects of real and reactive power flow through the local electric power system connected to the area electric power system. The method and system provides precise real and reactive power demand set point pairs; damping of real and reactive power fluctuations in the local electric power system; decoupling between real and reactive power demand response set points by means of a multivariable control system that uses time synchronized measurements of voltage and current phasors and their derivative information.

FIELD OF THE INVENTION

The invention relates to electrical power grids and, more specifically,to methods and systems for monitoring and controlling power flow in suchelectrical power grids.

BACKGROUND OF THE INVENTION

Distributed energy resources (DERs), which include renewable energypower sources, such as solar photovoltaic (PV) arrays and wind turbines,are often connected directly to distribution systems that are part of anarea electric power system (EPS). A large fraction of renewable energyresources will be installed in utility and customer owned distributionsystems as individual States try to attain their Renewable PortfolioStandards (RPS). At 50% or greater total renewable generation, it willbe difficult to control frequency and voltage to within acceptablestandards without active feedback controls. Additionally, some citiessuch as San Diego are planning on having 100 percent renewable energywithin its city limits by 2035. Many of the renewable power sources willcome from small residential rooftop solar systems operating in lowvoltage distribution systems. There will be many independentparticipants installing renewable DERs without knowledge of the impacton the grid of the distributed resources and without adequate control oflocal frequency and voltage. The renewable energy resources (Solar PV,fuel cell, battery, wind) have little or no inertia since they areconnected to a power electronics device that converts DC power into ACpower. Diesel generators, on the other hand, have inertia and willcontribute this to the adjacent connected grid load. Controllable loadscan also be considered DERs since their power consumption can beregulated thus providing an additional means of control and providinginertia from the load side. These forms of DERs have higher inertialoads than typical renewable generation; however, they both should beused in a coordinated control system to regulate the frequency andvoltage of the local EPS.

Low inertia systems are difficult to control compared to systems withhigh inertia from rotating energy sources. The IEEE 1547.4 standardsclearly point out the sensitivity of DERs to instability and voltagestability issues in the presence of low inertia generation sources. Lackof control of the power characteristics DER power injection can causelarge variations in frequency or voltage exceeding standards that cancause the feeder or substation to disconnect from the area EPS. In atypical distribution feeder, one or more DERs may supply up to 10 MW ofpower. With adequate control and coordination, one or more DERs incombination with multiple feeders can form the basis of a microgrid.

U.S. Pat. No. 8,457,912 describes a method of creating a smooth anglefrom the discontinuous angle measured from the PMU. The method includesdetecting the change in direction of the angle and compensating for thediscontinuous wrap at plus or minus 180°. This method is required inorder to compute a smooth angle and a smooth angle difference that areused in the control system.

U.S. Pat. No. 8,498,752 describes a method of decoupling real andreactive power from changes in voltage and angle. It also teaches thatthe control system can be reversed so that the voltage and angle can becontrolled to a constant value by simultaneously changing the real andreactive power. The controller uses the basic principle that theresponse to real and reactive power injection causes a simultaneouschange to voltage and angle by fundamental physics known as Ohm's law.

The controller also assumes that the network impedance is constant andis a known value. The nonlinear systems are linearized around andoperating point resulting in a linear set of equations that are used inthe coupled controller. The patent teaches how the system can belinearized around an operating point and then any linear control SystemTechnology can be used to configure the controller.

U.S. patent application Ser. No. 14/956,684 teaches how multipledecoupled controllers can be configured in cascade mode to form ahierarchical control system. It provides an explicit example of how theSmith predictor controller could be used in the control system design.Additionally, the controller technology recommended is based on commonlyused proportional plus integral plus derivative control. The patent alsoteaches that the controls can be reversed so that the input and outputvariables at any one level can be reversed to form a set of hierarchicalcontrollers that can be configured in cascade mode to perform a numberof control system functions in Electric Power Networks.

SUMMARY OF THE INVENTION

The present invention relates to the use of a hierarchy of 2×2 decoupledcontrollers for controlling DERs connected to power grids. These DERscan be any combination of very low inertia DERs such as batteries andsolar PV arrays or slower responding DERs such as controllable loads inbuildings, conventional thermal inertia based generation or any mix ofhydro or wind generation with differing dynamic response. This inventionis related to prior work by one of the present inventors, namely, twoU.S. Pat. Nos. 8,498,752 and 8,457,912 and patent application U.S.patent Ser. No. 14/956,684, all of which are incorporated herein byreference. These teach how to decouple voltage and frequency and unwrapangle information from phasor measurement units (PMUs). The controls areaccomplished by using real time feedback control to regulate power flowvoltage and frequency (or angle) by adjusting real and reactive powerdemand set point pairs of DERs.

The teachings of the present invention improves and extends the aboveprior work in various significant ways. The teachings of the presentinvention provide a unique and innovative approach to using phasormeasurements directly in the control system. It also clearly teaches howthe controller can be designed without the explicit knowledge of theimpedance between two points in the power grid. This invention alsoteaches that the phasor controls can also be reversed and used in acascade mode. It also teaches that both the voltage phasors and currentphasors can be used as the primary measured variables in the controlsystem. In both cases, the control system is linear in the phasorvariables. This makes the controller easy to tune and configure usingconventional off the shelf control System Technology tools. Other uniquefeatures of the invention include the use of a filtered output from thecontroller, a use of a filtered derivative to compute the derivativeaction of the controller and the separation of the proportional andintegral part of the controller. Additionally, a unique method ofdecoupling is performed outside of the controller function in a separatedecoupling matrix. This makes the coupling far easier than in priorwork. Additionally, the present invention explicitly outlines the use ofsetpoint feed forward control, which is important for fast response tothe disturbances in the Power Network. Additionally, the controllerexplicitly includes a method of modeling the process that includes fourlinear filters that are used to represent the dynamic state of thecontrol system. These filters are extensively used in the controllersuch that the internal functionality of the controller has a limitednumber of independent control system objects. This current controllercan be configured so that it operates as a controller without using theSmith predictor, a controller that can be used specifically for powercontrol, and a controller that can be configured as two independentsingle input single output controllers. The present invention alsoexplicitly describes how the controller can be configured to control thecurrent and power angle or the voltage and voltage angle. Thisflexibility is useful in the control of microgrids.

According to teachings of the present invention, the controller in U.S.Pat. No. 8,498,752 can be re-structured to control voltage magnitude andvoltage angle and or the current magnitude and power angle by adjustingreal and reactive power setpoint pairs of the DER, and the controls canbe reversed and used to control real and reactive power using voltagemagnitude and voltage angle or current magnitude and power anglesetpoint pairs. The control system uses the unwrapped angle rather thana frequency signal derived from the angle measurement. The usage of thissystem automatically controls frequency since it is defined as the rateof change of voltage angle and, hence, if the angle is constant, bydefinition, the frequency is constant. According to teachings of thepresent invention, the controller may be operated at higher speedscompared to conventional Energy Management Systems, and timesynchronized data may be used in the control system operations. Thepresent invention provides an enhancement to traditional real andreactive power control that currently uses slow speed andnon-synchronized open loop control.

In one aspect, the invention uses time synchronized real and reactivepower measurements in a high-speed feedback control system designed tomitigate disturbances while regulating the system to a specified realand reactive power setpoints. It also includes a control system thatcontrols the state or the power of the system using the same controllerstructure. It incorporates a separate proportional-integral combinedwith a derivative filter to mitigate power grid disturbances and also anoutput filter to adjust the output signal according to the responsecharacteristics of the DERs. The invention provides an increase in theperformance of the control system by using decoupled time synchronousinput and output measurements. It uses either the decoupled pair(voltage magnitude and voltage angle) or the decoupled pair (currentmagnitude and power angle) as measured variables to precisely controlreal and reactive power while operating at high rates. This controlstructure can be reversed to form a decoupled control system regulatingthe pair (real power and reactive power) to obtain decoupled phasoroutput setpoints pairs for either (current magnitude and power angle) or(voltage magnitude and voltage angle.) These identically structuredcontrollers can be used in cascade mode to directly control the powerdemand of the DER.

According to another aspect, the invention provides a control systemincluding a first 2×2 decoupled controller that controls currentmagnitude and power angle (difference between the voltage angle andcurrent angle) by adjusting real and reactive power using real timefeedback, and a reverse 2×2 decoupled controller that controls real andreactive power by adjusting current magnitude and power angle setpointsusing real time feedback. The first 2×2 decoupled controller and second2×2 decoupled controller can be used independently or where the secondthe second 2×2 decoupled controller is a supervisory controller of thefirst 2×2 decoupled controller.

In some embodiments, the first 2×2 decoupled controller is a unit levelcontroller directly manipulating devices that control the supply and/ordemand of a power bus, and the second 2×2 decoupled controller controlsreal and reactive power of the grid to specified setpoints by adjustingcurrent magnitude and power angle setpoints of one or more unitcontrollers using real time feedback. In this case, the supervisorycontroller has specified real and reactive power setpoints.

In one aspect, the invention provides a method for decoupling control ofreal and reactive power of a local electrical power system havingmultiple distributed energy resources at non-co-located points. Themultiple distributed energy resources may include a combination ofenergy generation devices, controllable energy loads, and energy storagedevices. The method includes feeding back time-synchronized measurementsof voltage phasors and current phasors from multiple phasor measurementunits to multivariable linear decoupling controllers; and controllingthe distributed energy resources by the multivariable linear decouplingcontrollers, wherein the controlling comprises sending to thedistributed energy resources real and reactive power setpoint pairsderived from the time-synchronized measurements of voltage phasors andcurrent phasors using linear control.

The feeding back may include feeding back phasor measurements frommultiple level 1 controllers to a level 2 controller, such that themultivariable linear decoupling controllers form a hierarchical feedbackcontrol system; converting measured real and reactive power values tocurrent and power angle phasors; and/or converting measured real andreactive power values to voltages and voltage angle differences betweenpoints of interest and the distributed energy resources.

Controlling the distributed energy resources by the multivariable lineardecoupling controllers may include: using a proportional-integralcontroller combined with a derivative filter to mitigate power griddisturbances, and an output filter to adjust output setpoint pairsaccording to a response characteristics of the distributed energyresources; using an internal predictive model to account for systemdynamics and transport delay in obtaining phasor feedback; using a feedforward filter for providing a faster phasor control in response toimmediate set point changes; and/or computing the real and reactivepower setpoint pairs to achieve a predetermined power control at a PointOf Interest.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic block diagram of a traditional power controlledsingle Distributed Energy Resource (DER), accepting a real/reactivepower reference input for the controlled DER and producing areal/reactive power output at the DER, monitored and controlled using apower controller that produces real/reactive power input at the DER anduses feedback of the produced real/reactive power output at the DER.

FIG. 2 is a schematic block diagram of a phasor controlled singleDistributed Energy Resource (DER), accepting a real/reactive powerreference input for the controlled DER and producing a real/reactivepower output at the DER, monitored and controlled by a phasor controllerthat produces real/reactive power input at the DER and uses feedback ofthe produced real/reactive power output at the DER, according to anembodiment of the present invention.

FIG. 3 is a schematic block diagram of a Level 1 phasor controlledsingle Distributed Energy Resource (DER), accepting a real/reactivepower reference input for the controlled DER and producing areal/reactive power output at the DER, monitored and controlled by aLevel 1 phasor controller that produces real/reactive power input at theDER and uses feedback of the produced phasor output at the DER,according to an embodiment of the present invention.

FIG. 4 is a schematic block diagram of a Level 2 phasor controlledmultiple Distributed Energy Resource (DER), accepting a real/reactivepower reference input at a Point Of Interest (POI) and producing areal/reactive power output at the POI, monitored and controlled by aLevel 2 phasor controller that distributes and schedules real/reactivepower input at the multiple DER and uses feedback of the produced phasoroutput at the POI, according to an embodiment of the present invention.

FIG. 5 is a schematic block diagram of a voltage phasor control multipleDistributed Energy Resource (DER), accepting a voltage phasor referenceinput at a Point Of Interest (POI) and producing a voltage phasor outputat the POI, monitored and controlled by a voltage phasor controller thatdistributes and schedules voltage amplitude input and voltage phaseangles at the multiple DER and uses feedback of the produced phasoroutput at the POI, according to an embodiment of the present invention.

FIG. 6 is a schematic block diagram of the preferred embodiment of thecontrol algorithms inside the phasor controller used in Level 1 andLevel 2 phasor controlled Distributed Energy Resources, according to anembodiment of the present invention.

FIG. 7 is a schematic block diagram of an alternative embodiment of thecontrol algorithms inside the phasor controller used in Level 1 andLevel 2 phasor controlled Distributed Energy Resources, according to anembodiment of the present invention.

FIG. 8 is a schematic diagram of an area EPS connected to a local EPShaving a hierarchical control of DERs, according to an embodiment of thepresent invention.

DETAILED DESCRIPTION Nomenclature and Abbreviations

V—voltage amplitude measured in volt

β—unwrapped voltage phase angle, measured in radians

v—voltage phasor consisting of (V,β) pair

f—power frequency

I—current amplitude measured in ampere

γ—unwrapped current phase angle measured in radians

i—current phasor consisting of (I,γ) pair

α—power angle and defined as difference between β and γ

I_(p)—current power phasor I_(p)=Ie^(jα)

I_(c)=real part of current power phasor

I_(s)—imaginary part of current power phasor

VA—Voltage Ampere

P—real power, measured in Watt.

Q—reactive power, measured in VA

S—apparent power (complex number S=P+jQ)

Z—complex impedance Z=|Z|e^(jθ)

|Z|—absolute value of complex impedance

θ—angle of impedance Z

δ—difference between voltage angles β_(b) at location b and voltageangle β_(a) at location a in EPS

a tan 2( )—four quadrant inverse tangent

Area EPS—the main power grid that connects many local EPS

Local EPS—a local power grid such as a Micro grid

Macro grid—the main power grid to which the microgrid is attached

Micro grid—a collection of loads and resources that act as a singlepoint of control to the macro-grid and can disconnect and re-connect tothe macro-grid

Area EPS is generally the part the network supplying power to themicrogrid. Often this is at a higher voltage (69 kV) compared to thelocal EPS (12 kV). There is a transformer and a breaker between the two.The breaker a remotely operated switch that separates the local EPS fromthe area EPS. The breaker separating the two grids is called a Point ofCommon Coupling if the local EPS is a microgrid. It is important thatthe local EPS can be continually connected to the area EPS, but ourcontroller provides demand regulation services to the local EPS. A localEPS could be a commercial or industrial building with solar PV and aBattery.POI—Point Of InterestPCC—Point of Common Coupling (which may refer to POI)DER—distributed energy resources, examples include Photovoltaic orBattery Inverter based systems, fuel cells, wind power, CHP such ascombined cycle gas turbine or micro generator, fuel cells and batteries.PMU—phasor measurement unitControl—the process of adjusting the input to a system to cause theoutput to achieve a specified setpoint.Setpoint—the specified value of an output variable in a processController—the system that compares the controller setpoint with theoutput variable and makes adjustments to the process input variables.This can be hardware or software. In this description, the controller issoftware.CDER—a controlled distributed energy resourceMDER—multiple distributed energy resourcesMIMO—Multi Input, Multi OutputPI—Proportional and IntegralFD—Filtered DerivativeRelation Between Phasors and Real/Reactive Power

The electric behavior at any Point Of Interest (POI) in a (single phase)Alternating Current (AC) electric power system (EPS) is characterized bya voltage of the format v(t)=V sin(2πft+β) and a current of the formati(t)=I sin(2πft+γ). The AC voltage magnitude V and voltage angle β,collectively called the voltage phasor v=(V,β) and the AC currentmagnitude I and current angle γ, collectively called the current phasori=(I,γ) are related through Ohm's law. In an EPS, the complex impedanceplays an important role in Ohm's law. In case the complex impedance is alinear (dynamic) system, the complex impedance can be represented by acomplex number |Z|e^(jθ) and denoted simply by the complex number Z withan absolute value of the impedance denoted by |Z| and a phase shift ofthe impedance denoted by θ. With the notion of a complex impedance Z,Ohm's law for a linear (dynamic) system states that the voltage phasor vand current phasor i are related via v=Zi. This makes the magnitude Vrelated to the current magnitude I via the equation V=|Z|I, whereas thevoltage angle β is related to the current angle γ via β=θ+γ due to thecomplex calculation v=Zi. The impedance Z in an EPS may refer to, but isnot limited to, an electrical source producing electrical power, anelectrical line transporting electrical power or an electrical loadconsuming electrical power.

As outlined in referenced U.S. Pat. No. 8,498,752, the AC voltagemagnitude V, voltage angle β, the AC current magnitude I, current angleγ, and the AC frequency f are available from Phasor Measurement Unitsdeployed in an EPS. The AC voltage magnitude V and voltage angle β arecollectively called the voltage phasor v and the voltage phasor v can berepresented by the pair v=(V,β) or the complex vector v=e^(jβ), where jis the complex number with j²=−1. Similarly, the AC current magnitude Iand current angle γ are collectively called the current phasor i and thecurrent phasor i can be represented by the pair i=(I,γ) or the complexvector i=e^(jγ). The voltage phasor v and current phasor i can be usedto obtain derivative information that may include, but is not limitedto, the real power P and reactive power Q that characterize theelectrical power flow from, through or into an impedance Z located inthe EPS.

In case the impedance Z=|Z|e^(jθ) between a location a and a location bin an EPS is known and characterized by its amplitude |Z| and its phaseangle θ, the real power P and reactive power Q flow through the knownimpedance from location a to location b can be computed by

$P = {{\frac{V_{a}V_{a}}{2{Z}}{\cos(\theta)}} - {\frac{V_{a}V_{b}}{2{Z}}{\cos\left( {\theta - \delta} \right)}}}$and$Q = {{\frac{V_{a}V_{a}}{2{Z}}{\sin(\theta)}} - {\frac{V_{a}V_{b}}{2{Z}}{\sin\left( {\theta - \delta} \right)}}}$where V_(a) and V_(b) are the voltage amplitudes respectively atlocation a and location b and where δ=β_(b)−β_(a), is the differencebetween voltage phase angle β_(b) at location b and voltage phase angleβ_(a), at location a. The above formula indicates that real P andreactive Q power flow between two locations in an EPS can be derivedfrom the equivalent impedance Z between the two locations in the powergrid and the voltage phasor measurements=(V_(a),β_(a)) and v_(b)=(V_(b),β_(b)) respectively at the two locations a and b in the EPS.

In case the power flow at a particular POI in the EPS needs to bemonitored and controlled, both the voltage the voltage phasor (V,β) andthe current phasor (I,γ) can be used to compute the real power P andreactive power Q. A particular POI in the EPS may include, but are notlimited to, the location of a Distributed Energy Resource (DER) in theEPS or a Point Of Interest (POI) in the EPS that may include the PointOf Interest (POI) where a local EPS connects to the main EPS. The realpower P and reactive power Q flow at a POI can be computed by

$P = {\frac{VI}{2}{\cos(\alpha)}}$ and$Q = {\frac{VI}{2}{\sin(\alpha)}}$where V and I are respectively the voltage amplitude V and the currentamplitude I at the POI, and the angle α=β−γ is the difference betweenvoltage phase angle β and the current phase angle γ at the POI. Theangle α is also referred to as the power angle α, as it directly relatedto the (normalized) size and direction of the real and reactive powerflow with cos(α) and sin(α) always in the range between −1 and 1. Basedon the power angle α we also define the notion of a current power phasorI_(p)=Ie^(jα) that combines the information on the current amplitude Iand power angle α.

FIG. 1 depicts the conceptual arrangement of a standard power-basedapproach to control a power source producing real/reactive AC power inan EPS via power feedback. As shown in the arrangement of FIG. 1, thepower source 1 conceptually accepts a real/reactive input pair denotedby in [P,Q] and will produce an actual real/reactive output pair at theDER denoted by DER [P,Q]. To ensure the produced real/reactive outputpair DER [P,Q] matches a desired reference real/reactive output pairdenoted by DER ref [P,Q] in FIG. 1, a power control 3 implements acontrol algorithm that compares DER ref [P,Q] and DER [P,Q] and producesthe real/reactive power input in [P,Q]. It is clear that the powercontrol algorithm is using feedback information of the producedreal/reactive power output (DER power feedback) to monitor and controlthe produced power at the output of the DER.

Although direct feedback information of power flow as illustrated inFIG. 1 is a viable approach to monitor and control the power flowproduced by a power source, the above formulae indicate thatreal/reactive power flow at a POI in a power grid can be deriveddirectly from the time synchronized measurements of the voltage phasorv=(V,β) and the current phasor i=(I,γ), collectively called the phasors.Therefore, the size and direction of real and reactive power flow at anyPOI in an EPS can be controlled by changing the voltage phasor v=(V,β)or the current phasor i=(I,γ) and in particular the power angle α=β−γand the product VI of the voltage amplitude V and current amplitude I.Although there seems to be no distinction between using phasors [v,i]information or real/reactive power [P,Q] information, there are threeclear advantages of using phasors [v,i] for (power) control instead ofusing the real/reactive power pair [P,Q].

The first advantage of using phasor [v,i] for feedback is due to thefact that phasors at different locations in an EPS may be linearly(dynamically) related. The linear relation is guaranteed provided theimpedance Z between the phasors is a linear dynamic system. However,even if Z is a linear dynamic impedance, the real/reactive power [P,Q]will always be a non-linear relation due to the product of voltagephasor v and current phasor i. For example, the voltage phasor v_(out)over a load modelled by the impedance Z_(L) and produced by a voltagesource v_(in) with a line impedance Z_(in) is given by v_(out)=Zv_(in)where

$Z = \frac{Z_{L}}{Z_{L} + Z_{i\; n}}$

If indeed Z is a linear dynamic impedance, the voltage phasor v_(out)depends linearly on the voltage phasor v_(in). Hence, using usingphasors [v,i] for feedback allows the use of linear control algorithmsto control phasor and the resulting power flow in an EPS.

The second advantage of using phasor [v,i] for feedback is due to thefact that the real/reactive power pair [P,Q] is inherently atrigonometric statically coupled pair and related via the apparent powerS=P+jQ and the power angle α mentioned above. This means that increasingthe size |S| of the apparent power may be done by either increasing thereal power P or the reactive power Q, but to maintain the same ratiobetween P and Q, any changes in P must be coupled to the changes in Q.This always requires the real/reactive power pair [P,Q] to be treated asa coupled pair during power control. Using phasors [v,i] for feedbackand in particular using either the current amplitude/power angle pair[I,α] or the Voltage amplitude/power angle pair [V, a] does not requirestatic coupling between a phasor amplitude and power angle pair.

The third advantage of using phasor [v,i] for feedback is due to thefact that the phasor pair [v,i] contains more information than thereal/reactive power pair [P,Q]. As shown below, power flow informationrepresented by the real/reactive pair [P,Q] does not contain fullinformation about the voltage v=(V,β) and current phasor i=(I,γ): onlythe phase difference α=β−γ (power angle) between the voltage angle β andthe current angle γ and the product VI of the voltage amplitude V andcurrent amplitude I can be reconstructed from the real/reactive pair[P,Q]. However, having access to the phasor pair [v,i] allowspower(flow) at a particular POI in an EPS to be computed, whereas theindividual voltage phasor v=(V,β) and current phasor i=(I,γ) alsocontain information about the individual voltage amplitude V, currentamplitude I and voltage angle β and current angle γ useful for voltageangle or current angle tracking control systems.

FIG. 2 depicts the conceptual arrangement of a phasor-based controlapproach to control the power source 2 which is a modified version ofpower source 1 shown earlier in FIG. 1. For notational convenience, theformulae for computing the real/reactive power pair [P,Q] on the basisof phasors pair [v,i] is denoted by the function PQ( ) and indicated bythe function blocks 6 and 8 in FIG. 2. The function operation[P,Q]=PQ(v,i) indicates that the (single phase) real/reactive power pair[P,Q] is computed from information of the voltage phasor v and currentphasor i according to P=VI/2·cos (a) and Q=VI/2·sin(α) in which α=β−γ.The computation of real/reactive power can easily be extended to commonthree phase AC system where three voltage and current phasors for eachphase are available.

Conversely, given a real and reactive power pair (P,Q) at any POI in theEPS, the power angle α=β−γ and the product VI of the voltage amplitude Vand current amplitude I and can be computed viaα=a tan 2(Q,P)andVI=2·√{square root over (P ² +Q ²)}where a tan 2( ) denotes the four quadrant inverse tangent, creating apower phase angle α in the interval between −π and π radians. The aboveformulae indicate that information on the real and reactive power pair[P,Q] is not sufficient to reconstruct the full information on thevoltage phasor v=(V,β) and/or the current phasor i=(I,γ). Only thedifference α=β−γ between the voltage angle β and the current angle γ andthe product |S|=VI of the voltage amplitude V and current amplitude Ican be reconstructed. However, additional information on either thevoltage phasor v=(V,β) or the current phasor i=(I,γ) suffices toreconstruct the phasor pair [v,i] from real and reactive power pair(P,Q).

For notational convenience, the inverse operation from the real andreactive power pair [P,Q] back to any information on the phasors will bedenoted by the function invPQ( ) and marked as function block 10 and 12in FIG. 2. The information on the phasors computed by the functioninvPQ( ) may use information on the voltage phasor v=(V,β) or thecurrent phasor i=(I,γ) and may also have different embodiments, alteringthe signals used in the internal phasor control 16 in FIG. 2.

In one embodiment called polar phasor current control, the functionoperation [I, α]=invPQ(P,Q) may refer to the computation of the polarcoordinates (I, α) representing the power angle α=β−γ and the currentamplitude I of the complex power current I_(p)=Ie^(jα) computed frominformation of the real power P and reactive power Q according to α=atan 2(Q,P) and I=2/V·√{square root over (P²+Q²)}.

In another embodiment function called rectangular current phasorcontrol, the operation [I_(c),I_(s)]=invPQ(P,Q) may refer to thecomputation of the rectangular coordinates [I_(c),I_(s)] representingthe real part I_(c)=I cos (α) and the imaginary part I_(s)=I sin (α) ofthe complex power current I_(p)=Ie^(jα) computed from information of thereal power P and reactive power Q according to I_(c)=2P/V and I_(s)=2Q/Vassuming the voltage V≠0.

It is worth noting that if the function invPQ( ) simply passes throughthe real and reactive power [P,Q]=invPQ(P,Q), the phasor control 16 inFIG. 2 has the result that power control 4 reduces back to the powercontrol 3 of FIG. 1. Clearly, the use of phasor control 16 allows fordifferent embodiments that exploit the three clear advantages of usingphasors [v,i] for (power) control instead of using the real/reactivepower pair [P,Q] as mentioned earlier. For notational convenience we usethe same notation of phasors [v,i] as the output of the function invPQ() marked as function block 12 in FIG. 2 to refer to the differentembodiments that convert information on real and reactive power pair[P,Q] back to any information on the phasors.

For comparison we now refer to both FIG. 1 and FIG. 2, where in FIG. 1the power source 1 and a power control 3 systems are present, while inFIG. 2 these are modified to become power source 2 and a power control 4systems. However, in FIG. 2 the invPQ ( ) function block 12 is placed atthe input of the phasor source 14 and PQ ( ) function block 8 is placedat the output of the phasor source 14. This concept allows the powersource 2 to be represented as a series connection of the invPQ ( )function block 12, a phasor source 14 and a PQ ( ) function block 8.Similarly, with the invPQ ( ) function block 10 in place at the input ofthe phasor control 16 and PQ ( ) function block 6 in place at the outputof the phasor control 16, internally the power control 4 can now berepresented as a series connection of the invPQ ( ) function block 10, aphasor control 16 and a PQ ( ) function block 6.

Although the external arrangement of power control using the novelphasor-based approach in FIG. 2 appears the same as in FIG. 1, theinternal phasor-based operation is significantly different. Theadvantage of separating the invPQ ( ) function block 10, the phasorcontrol 16 and the PQ ( ) function block 6 from the power control 4allows the phasor control algorithm in the phasor control 16 to bedesigned on the basis of phasor source 14. With the linear dynamicrelationship between phasors (v,i) in the presence of a linear impedanceZ in the EPS, the phasor control algorithm may be linear and will bemuch easier to design. Furthermore, due to trigonometric static couplingbetween P and Q in the real/reactive power pair [P,Q], the separation ofthe invPQ ( ) function block 10 and the PQ ( ) function block 6, adecoupling based phasor control system is provided in the form of thephasor control 16. However, the phasor-based approach in FIG. 2 is stillusing real/reactive power [P,Q] as feedback information and anadditional step is taken to also replace the feedback information on thereal/reactive power [P,Q] with feedback information on the actual phasor[v,i] to provide a true decoupling synchrophasor based control system.

Level 1 Control of a Controlled Distributed Energy Resource

FIG. 3 depicts the conceptual arrangement of a decoupling synchrophasorbased control system called the Level 1 Controlled Distributed EnergyResource or Level 1 CDER for short. The Level 1 indication is used todistinguish the hierarchical controller structure defined over severallevels to define a decoupling synchrophasor based control system formultiple distributed energy resources. The control algorithm in FIG. 3uses real-time feedback measurements of the phasors (V,β) and (I,γ) tocontrol real/reactive power pair (P,Q) at a POI in an EPS. As a result,the PQ( ) function block 8 has now been split from power source 14 usedearlier in FIG. 2 and direct DER phasor feedback information is sentback to the Level 1 Controller 18 in FIG. 3. The series connection ofthe invPQ( ) function block 12 and the phasor source 14 has beenlabelled Level 0 CDER 34 to distinguish this DER at the lower level 0from the phasor controlled DER at the higher level 1. The combination ofthe Level 0 CDER 34 along with the DER phasor information feeding backinto the Level 1 Controller 18 and producing real/reactive power inputDER [P,Q] 30 for the Level 0 CDER 34 is now indicated as a Level 1 CDER20 in FIG. 3. It should be noted that the Level 1 CDER 20 has the sameinput/output format as the Level 0 CDER 34, enabling the hierarchicalstructure of different controller levels.

The information and power flow of the Level 1 CDER 20 in FIG. 3 is asfollows. Starting from the left side of FIG. 3, the real/reactive powerreference signal labelled DER ref [P,Q] 22 feeds into the Level 1 CDER20 and then into the Level 1 Controller 18. In the Level 1 Controller 18first the real/reactive power reference signal DER ref [P,Q] 22 isconverted into a phasor reference signal DER ref [v,i] 24 via the invPQ() function block 10. The invPQ( ) function block 10 in FIG. 3 is thesame invPQ( ) function block 10 in FIG. 2. The invPQ( ) function block10 requires information on either the voltage phasor v=(V,β) or thecurrent phasor i=(I,γ) indicated by the (dotted) phasor informationsignal 26.

The phasor reference signal DER ref [v,i] 24 produced by the invPQ( )function block 10 in FIG. 3 may have different embodiments, altering thesignals used in the internal phasor control 16 in FIG. 3. In oneembodiment called polar phasor current control, the function operation[I, α]=invPQ(P,Q) may refer to the computation of the polar coordinates(I,α) representing the power angle α=β−γ and the current amplitude I ofthe complex power current I_(p)=Ie^(jα) computed from information of thereal power P and reactive power Q according to α=a tan 2(Q,P) andI=2/V·√{square root over (P²+Q²)}. In another embodiment function calledrectangular current phasor control the operation[I_(c),I_(s)]=invPQ(P,Q) may refer to the computation of the rectangularcoordinates [I_(c),I_(s)] representing the real part I_(c)=I cos (α) andthe imaginary part I_(s)=I sin (α) of the complex power currentI_(p)=Ie^(jα) computed from information of the real power P and reactivepower Q according to I_(c)=2P/V and I_(s)=2Q/V assuming the voltage V≠0.

Both the DER ref [v,i] 24 phasor reference signal and the DER [v,i] 28phasor feedback signal enter the phasor control 16 that will compute aphasor control signal. More details on the inner workings of phasorcontrol 16 is included in the discussion of FIG. 6 below.

The phasor control signal computed by the algorithm in phasor control 16is then converted again to an DER power input signal DER [P,Q] 30 viathe PQ( ) function block 6, defined also earlier in FIG. 2. The DERpower input signal DER [P,Q] 30 is processed by the invPQ( ) functionblock 12 and the phasor source 14, both defined earlier in FIG. 2, toproduce a phasor output DER [v,i] 28. The phasor output DER [v,i] 28 isnow fed back to the Level 1 controller 18 for continuous monitoring ofphasor behavior. Although not essential for the (feedback) operation ofthe phasor controller DER in FIG. 3, the phasor output DER [v,i] 28 canbe converted back to real/reactive power signal DER [P,Q] 32 via thesame PQ( ) function block 8 defined earlier in FIG. 2. The PQ( )function block 8 given in FIG. 3 can be used to compare the (tracking)performance of real/reactive power signal DER [P,Q] 32 with respect tothe real/reactive power reference signal DER ref [P,Q] 22.

The Level 1 CDER in FIG. 3 combines the benefits of the phasorcontrolled DER of FIG. 2 with phasor feedback to obtain more informationabout the individual voltage phasor signal v=(V,β) and current phasorsignal i=(I,γ). Although conceptually, the arrangement of power controlof the novel phasor-based approach in FIG. 3 is the same as in FIG. 2,the advantage of splitting the PQ ( ) function block 8 from the phasorsource 14 and providing direct phasor (v,i) feedback is that moreinformation is brought into the Level 1 controller 18. Both voltageangle β and current angle γ are now available instead of the power angleα=β−γ only. Furthermore, the separation allows the dynamics of thecontrol algorithm in the phasor control 16 to be designed on the basisof the dynamics of the phasor source 14.

As indicated earlier, with the linearity of the phasors (v,i) in thepresence of linear impedances Z in the EPS, such a control algorithmwill be much easier to design. In essence the feedback algorithm of theLevel 1 CDER 20 in FIG. 3 internally uses phasor information, while fromthe outside the benefits of the feedback control in terms of power flowcontrol can be observed from the real/reactive power signal DER [P,Q]32. The concept of phasor feedback and the use of linear controlalgorithms feedback can also be extended to the case of multiple DERs.

Control of Multiple Distributed Energy Resources for Phasor Tracking

FIG. 4 summarizes the concept of the preferred embodiment of adecoupling synchrophasor based control system for a Multiple DistributedEnergy Resources (MDER) that uses phasor signals for feedback to trackreal and reactive power reference signals. In the MDER 102, parallelplaced lower level Controlled Distributed Energy Resources (CDERs) arenow controlled by a Level 2 Controller 108. For reason of clarity andbrevity, FIG. 4, shows an embodiment where the MDER 102 has only twoparallel placed CDERs, given by the same generic function of the Level 1CDER 20 defined earlier in FIG. 3 and labeled Level 1 CDER #1 132 andLevel 1 CDER #2 134 in FIG. 4. However, embodiments of the same conceptmay include single or multiple instances of the Level 1 CDER 20 definedearlier in FIG. 3 and may also include single or multiple instances ofthe Level 0 CDER 34 defined earlier in FIG. 3.

As indicated earlier in FIG. 3, the Level 1 CDER 20 has the sameinput/output format as the Level 0 CDER 34 and the input to both a Level1 CDER 20 and a Level 0 CDER 34 is a real/reactive input (reference) DER[P,Q] 30 signal and the output of both a Level 1 CDER 20 and a Level 0CDER 34 is a DER [v,i] 28 phasor signal. This conformance and modularityallows a hierarchical control architecture at different levels, wheresimilar phasor control 16 defined earlier in FIG. 3 can be used. Thehierarchical control architecture at different levels is exploited inthe Level 2 CDER 106 given in FIG. 4. The main difference between theLevel 1 CDER 20 in FIG. 3 and the Level 2 CDER 106 in FIG. 4 is the factthat feedback information of a phasor signal POI [v,i] 142 at a Point OfInterest (POI) is used. Although a single POI phasor signal POI [v,i]142 is used for feedback, multiple DERs in the MDER 102 are controlledto a desired POI [v,i] 142 phasor signal at a POI to achieve the desiredreal/reactive power flow POI ref [P,Q] 104 at a POI.

The information and power flow of the Level 2 CDER 106 in FIG. 4 is asfollows. Starting from the left side of FIG. 4, the real/reactive POIpower reference signal labelled POI ref [P,Q] 104 feeds into the Level 2CDER 106 and then into the Level 2 Controller 108. In the Level 2Controller 108, first the real/reactive POI power reference signal POIref [P,Q] 104 is separated into individual real/reactive power referencesignals 112 and 114 for each Level 1 distributed energy resource by theload flow & DER scheduler functional block 110.

An embodiment of the load flow & DER scheduler 110 may include analgorithm that decides which DERs participate in the level 2 control andat what percentage they will contribute. More advanced logic or loadflow calculations can also be included in the load flow & DER schedulerfunctional block 110. The load flow and DER scheduler functions arecurrent state of the art functions and are not included in thisinvention. This function is shown to indicate that the power allocationto individual DERs need to be determined algorithmically. So any methodis suitable to be included.

The individual real/reactive power reference signals 112 and 114 foreach level 1 DER are converted to individual phasor reference signalsDER #1 ref [v,i] 116 and DER #2 ref [v,i] 118 by the separate invPQ( )function blocks 158 and 160 in FIG. 4. The invPQ( ) function blocks 158and 160 in FIG. 4 have the same generic functionality as the invPQ( )function block 10 defined earlier in FIG. 2 and FIG. 3, but requiresinformation on voltage phasor v=(V,β) or the current phasor i=(I,γ) ofeach DER indicated by the (dotted) phasor information signals 120 and122.

The phasor reference signals DER #1 ref [v,i] 116 and DER #2 ref [v,i]118 produced by the invPQ( ) function blocks 158 and 160 in FIG. 4 mayhave different embodiments, altering the phasor reference signals DER #1ref [v,i] 116 and DER #2 ref [v,i] 118 feeding into in the phasorcontrol 162 and 164 in FIG. 4. In one embodiment called polar phasorcurrent control, the function operation [I,α]=invPQ(P,Q) may refer tothe computation of the polar coordinates (I,α) representing the powerangle α=β−γ and the current amplitude I of the complex power currentI_(p)=Ie^(jα) computed from information of the real power P and reactivepower Q according to α=a tan 2(Q,P) and I=2/V·√{square root over(P²+Q²)}. In another embodiment function called rectangular currentphasor control the operation [I_(c),I_(s)]=invPQ(P,Q) may refer to thecomputation of the rectangular coordinates [I_(c),I_(s)] representingthe real part I_(c)=I cos (α) and the imaginary part I_(s)=I sin (α) ofthe complex power current I_(p)=Ie^(jα) computed from information of thereal power P and reactive power Q according to I_(c)=2P/V and I_(s)=2Q/Vassuming the voltage V≠0.

To use the individual phasor reference signals DER #1 ref [v,i] 116 andDER #2 ref [v,i] 118 for control in the phasor control 162 and 164, theDER #1 ref [v,i] 116 and DER #2 ref [v,i] 118 reference signals must becompared to individual phasor measurement signals DER #1 [v,i] 124 andDER #2 [v,i] 126 respectively. Since the separation of the individualphasor reference signals DER #1 ref [v,i] 116 and DER #2 ref [v,i] 118were generated by the load flow & DER scheduler functional block 110,the individual phasor measurement signals DER #1 [v,i] 124 and DER #2[v,i] 126 are generated by the same algorithm as used in the load flow &DER scheduler functional block 110 duplicated in FIG. 4 as block 100.

For that purpose, the POI phasor measurement signal POI [v,i] 142 isfirst sent through the PQ( ) functional block 146 to convert POI [v,i]142 into a POI real/reactive power that is then subjected to the loadflow & DER scheduler 100. For the conversion back to the individualphasor measurement signals DER #1 [v,i] 124 and DER #2 [v,i] 126, theinvPQ( ) function blocks 152 and 154 are used and require information oneither the voltage phasor v=(V,β) or the current phasor i=(I,γ) of eachCDER indicated by the phasor information signals 120 and 122. The samephasor information signals 120 and 122 were used earlier to create thesignals DER #1 ref [v,i] 116 and DER #2 ref [v,i] 118 via the invPQ( )function blocks 158 and 160.

The phasor reference signals DER #1 ref [v,i] 116, DER #2 ref [v,i] 118and the phasor feedback signals DER #1 ref [v,i] 124 and DER #2 ref[v,i] 126 enter the two individual phasor control 162 and 164 blocksthat will compute a phasor control signal. In some embodiments thefunctional block of the phasor control 162 and 164 may have the samecontrol algorithms as used in FIG. 3 for the Level 1 CDER 20, but mayhave different numerical values for the control algorithm, depending onthe dynamics of the level 1 CDER to be controlled at level 2. Forexample, the Level 1 CDER #1 132 may refer to the fast dynamics on abattery/inverter system, while the Level 1 CDER #2 134 may refer to theslower dynamics on a gas turbine/generator system. Due to the differencebetween in dynamics between Level 1 CDER #1 132 and Level 1 CDER #2 134,the phasor control 162 and 164 for each Level 1 CDER may be similar interms of algorithm, but different in terms of the numerical value usedin the algorithm. More details on the inner workings of phasor control162 and 164 block is included in the discussion of FIG. 6 below.

The phasor control signal computed by the algorithms in the individualphasor control 162 and 164 blocks are then converted to DER powerreference input signals DER #1 ref [P,Q] 128 and DER #2 ref [P,Q] 130via the PQ( ) function blocks 148 and 150. The PQ( ) function blocks 148and 150 in FIG. 4 have the same generic functionality as the PQ( )function block 6 in FIG. 2 and FIG. 3. The DER power reference inputsignal DER #1 ref [P,Q] 128 is processed by the Level 1 CDER #1 132 toan individual phasor output signal DER #1 [v,i] 136. Similarly, the DERpower reference input signal DER #2 ref [P,Q] 130 is processed by theLevel 1 CDER #2 134 to an individual phasor output signal DER #2 [v,i]138. The processing by the Level 1 CDER #1 132 or Level 1 CDER #2 134has the same generic functionality as the Level 1 CDER 20 definedearlier in FIG. 3.

The aggregated effect of the phasor output signals DER #1 [v,i] 136 andDER #2 [v,i] 138 is combined via the functional block representing theline impedances & grid dynamics 140 and results in a measurable phasorsignal at the Point Of Interest POI [v,i] 142 in FIG. 4. The lineimpedances & grid dynamics 140 in FIG. 4 is a lumped functional blockthat represents the interconnections and electrical parameters of theEPS that would lead to the Point Of Interest phasor signal POI [v,i] 142due to changes in the phasor output signals DER #1 [v,i] 136 and DER #2[v,i] 138 produced by the Level 1 CDER #1 132 and Level 1 CDER #2 134.The phasor signal POI [v,i] 142 is again fed back to the Level 2controller 108 for continuous monitoring of phasor behavior and controlpower flow. Although not essential for the (feedback) operation of theLevel 2 controller 108 in FIG. 4, the phasor signal POI [v,i] 142 can beconverted back to a POI real/reactive power signal POI [P,Q] 144 via thePQ( ) function block 146 given in FIG. 4. The PQ( ) function block 144given in FIG. 4 can be used to compare the (tracking) performance ofreal/reactive power signal POI [P,Q] 144 with respect to thereal/reactive power reference signal POI ref [P,Q] 104.

The voltage and current angles can be measured accurately using PMUs;however, as taught in the U.S. Pat. No. 8,457,912, the wrapping anglemeasurements of the phasors (V,β), (I,γ) are not smooth and thereforecannot be used for feedback control. This invention uses the smooth andunwrapped angle measurements as taught in U.S. Pat. No. 8,457,912 aswell as the time synchronized values of the phasors (V,β), (I,γ) and thereal/reactive power pair (P,Q) from a PMU or relay. These measurements,reported at high data rates, providing the means for the controllers toexecute at much shorter time intervals compared to existing grid andmacro-grid control systems.

The local EPS includes a number of protective relays, in particularacross the circuit breaker separating the area EPS from the local EPS.Most modern relays include PMU calculations and provide thesemeasurements at high data rates (60 Hz) to multiple clients. Thecontroller subscribes to these PMU measurement streams to obtain themeasurements needed for control. There are certain time delays inreceiving the data; hence the need for the Smith Predictorfunctionality. In other implementations, where electromechanical relaysare used, a new PMU measurement device is installed at the requiredlocation in the grid. These PMUs send the measurements to the controllerusing the same message protocols as used by the relays.

Control of Multiple Distributed Energy Resources for Voltage PhasorTracking

FIG. 5 summarizes the concept of an alternative embodiment of adecoupling synchrophasor based control system for a Multiple DistributedEnergy Resources (MDER) that uses phasor signals for feedback to track avoltage phasor reference signal ref [V,beta] 504. The voltage phasortypically consists of a (V,β) pair, where V is the voltage amplitude andβ is the voltage angle. Tracking the voltage amplitude V and voltageangle β phasor reference signal ref [V,beta] 504 at a POI of the EPS andespecially the Point of Common Coupling (PCC) of the EPS is important incase the EPS is disconnected from the main grid. Tracking the voltageamplitude V and voltage angle β of the main grid as a phasor referencesignal ref [V,beta] 504 allows quick connect and disconnect of the EPSfor islanding operations. Similar to FIG. 4, parallel placed ControlledDistributed Energy Resources (CDERs) in a single MDER 502 are nowcontrolled by the Voltage Phasor Controller 508. For reason of clarityand brevity, FIG. 5 shows an embodiment where the MDER 502 has only twoparallel placed CDERs and labeled CDER #1 532 and CDER #2 534 in FIG. 5.However, embodiments of the same concept may include single or multipleinstances of the CDER Controlled Distributed Energy Resources (CDERs).

It can be observed that the Voltage Phasor Controller 508 has the samegeneric functionality as the Level 2 CDER 106 in FIG. 4, however all ofthe PQ ( ) and invPQ( ) function blocks are removed. However, the phasorcontrol 562 and 564 in FIG. 5 have the same the same genericfunctionality the phasor control 162 and 164 in FIG. 4 promotingmodularity of the control architecture, where similar phasor control 16defined earlier in FIG. 3 can be used.

The information flow of the Voltage Control 506 in FIG. 5 is as follows.Starting from the left side of FIG. 5, the voltage phasor referencesignal labelled ref [V,beta] 504 feeds into the Voltage Control 506 andthen into the Voltage Phasor Controller 508. In the Voltage PhasorController 508 the voltage phasor reference signal ref [V,beta] 506 isseparated into individual voltage phasor reference signals DER #1 ref[V,beta] 516 and DER #2 ref [V,beta] 518 by the Voltage Phasor Schedulerfunctional block 510.

An embodiment of the Voltage Phasor Scheduler 510 may include analgorithm that decides which DERs participate in the voltage phasorcontrol and at what percentage they will contribute. More advanced logicor load flow calculations can also be included in the Voltage PhasorScheduler functional block 510.

To use the individual voltage phasor reference signals DER #1 ref[V,beta] 516 and DER #2 ref [V,beta] 518 for control in the phasorcontrol 562 and 564, the DER #1 ref [V,beta] 516 and DER #2 ref [V,beta]518 reference signals must be compared to individual voltage phasormeasurement signals DER #1 [V,beta] 524 and DER #2 [V,beta] 526respectively. Since the separation of the individual phasor voltagereference signals DER #1 ref [V,beta] 516 and DER #2 ref [V,beta] 518were generated by the Voltage Phasor Scheduler functional block 510, theindividual voltage phasor measurement signals DER #1 [V,beta] 524 andDER #2 [V,beta] 526 are generated by the same algorithm as used in theVoltage Phasor Scheduler functional block 510 duplicated in FIG. 5 asblock 500 with as input the POI voltage phasor feedback measurementsignal POI [v,beta] 542.

The phasor reference signals DER #1 ref [V,beta] 516, DER #2 ref[V,beta] 518 and the phasor feedback signals DER #1 ref [V,beta] 524 andDER #2 ref [V,beta] 526 enter the two individual phasor control 562 and564 blocks that will compute a phasor control signals DER #1 [V,f] 528and DER #2 [V,f] 530 where the variable f now refers to the frequency ofthe Voltage phasor. Conversion to frequency is done to accommodate theinput to the voltage sources CDER #1 532 and CDER #2 534 that againproduce a voltage phasor DER #1 [V,beta] 536 and voltage phasor DER #2[V,beta] 538. CDERs such as inverters typically allow independentspecification of Voltage amplitude V and frequency f of the AC voltagesignal. In some embodiments the functional block of the phasor control562 and 564 may have the same control algorithms as used in FIG. 4phasor control 162 and 164 but may have different numerical values forthe control algorithm, depending on the dynamics of the CDER to becontrolled. More details on the inner workings of phasor control 562 and564 block is included in the discussion of FIG. 6 below.

The aggregated effect of the voltage phasor DER #1 [V,beta] 536 producedby the voltage source CDER #1 532 and the voltage phasor DER #2 [V,beta]538 produced by the voltage source CDER #2 534 is combined via thefunctional block representing the line impedances & grid dynamics 540and results in a measurable voltage phasor signal POI [V,beta] 542 atthe Point Of Interest in FIG. 5. The line impedances & grid dynamics 540in FIG. 5 is a lumped functional block that represents theinterconnections and electrical parameters of the EPS that would lead tothe Point Of Interest phasor signal POI [V,beta] 542 due to changes inthe phasor output signals DER #1 [V,beta] 536 and DER #2 [V,beta] 538produced by the voltage sources CDER #1 532 and CDER #2 534. The voltagephasor signal POI [V,beta] 542 at the POI is again fed back to theVoltage Controller 508 for continuous monitoring of voltage phasorbehavior and track voltage amplitude V and voltage angle β.

Phasor Controller

FIG. 6 summarizes the concept of the preferred embodiment of the phasorcontrol 264 which implements the functionality of the phasor control 16in FIG. 2 and FIG. 3, the phasor controls 162 and 164 in FIG. 4 and thephasor controls 562 and 564 in FIG. 5.

The preferred embodiment of phasor control 264 is a two-input,two-output decoupling synchrophasor based control algorithm thatcomputes a phasor control output signal DER [v,i] 256 from a phasorreference signal ref [v,i] 210 and a phasor feedback data [v,i] 202. Thephasor control 264 also includes a simulation signal 204 and aprediction 206 signal produced by a predictive model 208 to account fortransport delay in obtaining the phasor feedback data [v,i] 202. Analternative embodiment of the phasor control 264 is given in the phasorcontrol 364 in FIG. 7 where the predictive model 208 has beeneliminated.

The information and power flow of the phasor control 264 in FIG. 6 is asfollows. Starting from the left side of FIG. 6, both the phasorreference signal ref [v,i] 210 and the phasor feedback data [v,i] 202enter the phasor control 264. In comparison with FIG. 3, the phasorreference signal ref [v,i] 210 may represent the phasor reference signalDER ref [v,i] 24 in FIG. 3. In comparison with FIG. 4, the phasorreference signal ref [v,i] 210 may represent the phasor reference signalDER #1 ref [v,i] 116 or the phasor reference signal DER #2 ref [v,i] 118in FIG. 4.

In the phasor control 264 of FIG. 6, first the difference between thephasor reference signal ref [v,i] 210 and the phasor feedback data [v,i]202 is computed by the difference junction 214 leading to the phasorerror signal 216. The simulation signal 204 is added to the error signal216 by the summing junction 218 leading to the simulation error signal220. Subsequently, the difference between the simulation error signal220 and the prediction signal 206 produced by the difference junction222 leads to the control input signal 224 that is fed into the diagonalPI controller 226. At the same time, the prediction signal 206 is fedinto the diagonal FD controller 228.

The role of the predictive model 208 is clear from the above describedsignal path. If the predictive model 208 provides an accurate simulationthat includes the same transport delay 230 and the same dynamicsmodelled by the dynamic model 232 as seen in the phasor feedback data[v,i] 202, then the simulation error signal 220 would be zero and onlythe prediction signal 206 will appear in the control input signal 224.Since the prediction signal 206 is equivalent to the simulation signal204, but without the transportation delay, the effect of transport delayin the phasor feedback data [v,i] 202 is completely compensated for, asonly the prediction signal 206 will appear in the control input signal224 that is fed into the diagonal PI controller 226. At the same time,the same prediction signal 206 is fed into the diagonal FD controller228. As a result, the predictive model 208 also known as a SmithPredictor is an important ingredient of the decoupling synchrophasorbased control algorithm used in the phasor control 264.

The diagonal PI controller 226 is a Proportional Integral (PI)controller. One embodiment of the diagonal PI controller 226 is thecomputation of the PI control output signal 234 as the sum of aproportional gain K_(p) amplified control input signal 224 and anintegral gain K_(i) amplified time integrated control input signal 224.Other embodiments may include other linear combinations of a gainamplified control input signal 224 and time integrated control inputsignal 224 implemented in discrete-time filters.

The diagonal FD controller 228 is a Filtered Derivative (FD) controller.One embodiment of the diagonal FD controller 228 is the computation ofthe FD control output signal 236 as a derivative gain K_(d) amplifiedfiltered prediction signal 206. In the alternative embodiment of thephasor control 264 in FIG. 6, the diagonal FD controller 228 may be aderivative gain K_(d) amplified filtered phasor feedback data [v,i] 202implemented in discrete-time filters. Conventionally, the derivativeoperates on the error signal. In our case, in contrast, it operates onmeasured or predicted signal. The derivative contribution is notaffected by setpoint changes that cause large output changes. Ourcontroller responds to process disturbances rather than setpointchanges. We also have setpoint feedforward term for handing setpointchanges.

Worth noting is the fact that both the control input signal 224, theprediction signal 206 and the phasor feedback data [v,i] 202 are (atleast) two dimensional input signals. As indicated earlier, in oneembodiment called polar phasor current control, the phasor feedback data[v,i] 202 may refer to the polar coordinates (I,α) representing thepower angle α=β−γ and the current amplitude I of the complex powercurrent I_(p)=Ie^(jα). In another embodiment called rectangular currentphasor control the phasor feedback data [v,i] 202 may refer to therectangular coordinates [I_(c),I_(s)] representing the real part I_(c)=Icos (α) and the imaginary part I_(s)=I sin (α) of the complex powercurrent I_(p)=Ie^(jα).

Given the fact that the control input signal 224 is at least a twodimensional signal, the diagonal PI controller 226 is a ProportionalIntegral (PI) controller that operates on each of the two signalsincluded in the two dimensional control input signal 224 independently.The independent operation maintains decoupling between each of the twosignals included in the two dimensional control input signal 224.Similarly, the diagonal FD controller 228 is a Filtered Derivative (FD)controller that operates on each of the two signals included in the twodimensional prediction signal 206 or the phasor feedback data [v,i] 202independently. The independent operation maintains decoupling betweeneach of the two signals included in the two dimensional control inputsignal 224.

Further decoupling is accomplished in the phasor control 264 of FIG. 6by sending a linear combination of the PI control output signal 234 andthe FD control output signal 236 produced by the difference or summingjunction 238 as a control signal 240 to a multi-input, multi-outputdecoupling filter 242. The preferred embodiment of the decoupling filter242 includes an output filter that can adjust the output signalaccording to the characteristics of the DER and is a multivariabledynamic system that aims to decouple the phasor feedback signal [v,i]either at the DER at Level 1 or at the POI at Level 2 control. Thedecoupling and output filters are combined into one filter for each ofthe elements in the decoupling matrix. This takes into account thedynamic decoupling and the output filters. The output filter is used toremove signals that the DER would not be able to respond to. Forexample, a rotating generator would not be able to respond to a 60 Hzvarying signal, so this high frequency information is filtered out forthis device. On the other hand, an inverter can respond to highfrequency commands, and thus its output filter would be a high passfilter. That is, it filters out the low frequency content of the outputsignal. Thus, fast control signals go to inverters and slow controlsignals go to generators. This is not commonly done in control systemsin industry and provides distinct advantages. An alternative embodimentof the decoupling filter 242 is to configure it as two single input andsingle output (SISO) controllers.

The output signal 244 of the decoupling filter 242 is combined by thesumming junction 246 with the feedforward control signal 248 of thefeedforward filter 250. The feedforward filter 250 directly takes thephasor reference signal ref [v,i] 210 to generate the feedforwardcontrol signal 248. The feedforward filter 250 in the phasor control 264allows the control signals to directly respond to any changes in thephasor reference signal ref [v,i] 210 without first having to go throughthe diagonal PI controller 226 and may allow for a faster phasor controlin response to set point changes in the phasor reference signal ref[v,i] 210 signal. The preferred embodiment of the feedforward filter 250has the same generic functionality as the decoupling filter 242: amultivariable dynamic system that also aims to decouple the real andreactive output signal [P,Q] either at the DER at Level 1 or at the POIat Level 2 control. An alternative embodiment of the feedforward filter250 is a fixed matrix gain to maintain or promote statically decoupledphasor feedback signal [v,i] either at the DER at Level 1 or at the POIat Level 2.

The final stage of the phasor control 264 of the preferred embodiment ofFIG. 6 is to send the summation signal 252 obtained by summing junction246 to a phasor saturation 254 to limit the phasor control output signalDER [v,i] 256. The phasor saturation may have different embodiments andcan limit the range or rate of change of the power angle α, the maximumcurrent amplitude I, and/or the maximum and minimum rectangularcoordinates [I_(c),I_(s)] representing the real part I_(c)=I cos (α) andthe imaginary part I_(s)=I sin (α) of the complex power currentI_(p)=Ie^(jα) or any variations of these signals and/or their rate ofchange. In FIG. 6 the phasor control output signal DER [v,i] 256 is inturn used to produce the simulation 204 and prediction 206 signals tocompensate for actual transport delay 230 using a dynamic model 232 thatmodels the dynamics in the phasor feedback data [v,i] 202.

FIG. 7 summarizes the concept of the alternative embodiment of thephasor control 364 which implements the functionality of the phasorcontrol 16 in FIG. 2 and FIG. 3 and the phasor controls 162 and 164 inFIG. 4. The alternative embodiment of phasor control 364 is also atwo-input, two-output decoupling synchrophasor based control algorithmthat computes a phasor control output signal DER [v,i] 356 from thephasor reference signal ref [v,i] 310 and the phasor feedback data [v,i]302. In the alternative embodiment of the phasor control 364 is given inFIG. 7 the predictive model 208 of the preferred embodiment of FIG. 6has been eliminated.

The information and power flow of the phasor control 364 in FIG. 7 is asfollows. Starting from the left side of FIG. 7, both the phasorreference signal ref [v,i] 310 and the phasor feedback data [v,i] 302enter the phasor control 364. In comparison with FIG. 3, the phasorreference signal ref [v,i] 310 may represent the phasor reference signalDER ref [v,i] 24 in FIG. 3. In comparison with FIG. 4, the phasorreference signal ref [v,i] 310 may represent the phasor reference signalDER #1 ref [v,i] 116 or the phasor reference signal DER #2 ref [v,i] 118in FIG. 4.

In the phasor control 364 of FIG. 7, first the difference between thephasor reference signal ref [v,i] 310 and the phasor feedback data [v,i]302 is computed by the difference junction 314 leading to the phasorerror signal 324. This signal is fed into the diagonal PI controller326.

The diagonal PI controller 326 is a Proportional Integral (PI)controller. One embodiment of the diagonal PI controller 326 is thecomputation of the PI control output signal 334 as the sum of aproportional gain K_(p) amplified control input signal 324 and anintegral gain K_(i) amplified time integrated control input signal 324.Other embodiments may include other linear combinations of a gainamplified control input signal 324 and time integrated control inputsignal 324 implemented in discrete-time filters.

The diagonal FD controller 328 is a Filtered Derivative (FD) controller.One embodiment of the diagonal FD controller 328 is the computation ofthe FD control output signal 336 as a derivative gain K_(d) amplifiedhigh pass phasor feedback data [v,i] 302. In the alternative embodimentof the phasor control 364 in FIG. 7, the diagonal FD controller 328 maybe a derivative gain K_(d) amplified high pass filtered phasor feedbackdata [v,i] 302 implemented in discrete-time filters.

Worth noting is the fact that both the control input signal 324, and thephasor feedback data [v,i] 302 are (at least) two dimensional inputsignals. As indicated earlier, in one embodiment called polar phasorcurrent control, the phasor feedback data [v,i] 302 may refer to the tothe polar coordinates (I,α) representing the power angle α=β−γ and thecurrent amplitude I of the complex power current I_(p)=Ie^(jα). Inanother embodiment called rectangular current phasor control the phasorfeedback data [v,i] 302 may refer to the rectangular coordinates[I_(c),I_(s)] representing the real part I_(c)=I cos (α) and theimaginary part I_(s)=I sin (α) of the complex power currentI_(p)=Ie^(jα).

Given the fact that the control input signal 324 is at least a twodimensional signal, the diagonal PI controller 326 is a ProportionalIntegral (PI) controller that operates on each of the two signalsincluded in the two dimensional control input signal 324 independently.The independent operation maintains decoupling between each of the twosignals included in the two dimensional control input signal 324.Similarly, the diagonal FD controller 328 is a Filtered Derivative (FD)controller that operates on each of the two signals included in the twodimensional prediction signal 306 or the phasor feedback data [v,i] 302independently. The independent operation maintains decoupling betweeneach of the two signals included in the two dimensional control inputsignal 324.

Further decoupling is accomplished in the phasor control 364 of FIG. 7by sending the difference (or sum) of the PI control output signal 334and the FD control output signal 336 produced by the difference orsumming junction 338 as a control signal 340 to a multi-input,multi-output decoupling filter 342. The preferred embodiment of thedecoupling filter 342 includes an output filter that can adjust theoutput signal according to the characteristics of the DER and is amultivariable dynamic system that aims to decouple the real and reactiveoutput signal [P,Q] either at the DER at Level 1 or at the POI at Level2 control. An alternative embodiment of the decoupling filter 342 is afixed matrix gain to statically decouple the phasor feedback data [v,i]either at the DER at Level 1 or at the POI at Level 2.

The output signal 344 of the decoupling filter 342 is combined by thesumming junction 346 with the feedforward control signal 348 of thefeedforward filter 350. The feedforward filter 350 directly takes thephasor reference signal ref [v,i] to generate the feedforward controlsignal 348. The feedforward filter 350 in the phasor control 364 allowsthe control signals to directly react to any changes in the phasorreference signal ref [v,i] 310 without first having to go through thediagonal PI controller 326 and may allow for a faster phasor control inresponse to set point changes in the phasor feedback signal [v,i] 302.The preferred embodiment of the feedforward filter 350 is similar to thedecoupling filter 342: a multivariable dynamic system that also aims todecouple the phasor feedback signal [v,i] either at the DER at Level 1or at the POI at Level 2 control. An alternative embodiment of thefeedforward filter 350 is a fixed matrix gain to maintain or promotestatically decoupled the phasor feedback data [v,i] either at the DER atLevel 1 or at the POI at Level 2.

The final stage of the phasor control 364 of the alternative embodimentof FIG. 7 is to send the summation signal 352 obtained by summingjunction 346 to a phasor saturation 354 to limit the phasor controloutput signal DER [v,i] 356. The phasor saturation may have differentembodiments and can limit the range or rate of change of the power angleα, the maximum current amplitude I, and/or the maximum and minimumrectangular coordinates [I_(c),I_(s)] representing the real part I_(c)=Icos (α) and the imaginary part I_(s)=I sin (α) of the complex powercurrent I_(p)=Ie^(jα) or any variations of these signals and/or theirrate of change.

The functional blocks described herein can best be implemented incommercial computing platforms such as advanced Programmable LogicControllers (PLCs) or in industrial grade PCs such as the SEL 3355 thatruns multiple tasks, one of which is the controller. The controllerprocessing functionality can be written in any computer language, butone implementation is using C++ running on Windows or Linux operatingsystems. The output commands from then controller may use standardcontrol protocols such as IEC 61850 Goose or Modbus over Ethernet. Inorder to maintain high security, fiber optic connections are generallyused between the controller platform and the inverter device that isused to control the real and reactive power flow to the local EPS. Forexample, the PQ( ) and invPQ( ) functions are preferably implementedusing the standard trigonometry and square root functions provided inthe computer language used to implement the controller.

FIG. 8 shows the relationship between the area Electric Power System(EPS) 800 and a local EPS 802. Two local EPS systems 802 and 804 areshown connected to the area EPS 800. An electrical disconnect switch 806is shown between the area EPS 800 and the local EPS 802. This is calledthe Point of Common Coupling. When this switch is opened, the local EPS802 must maintain its own supply and demand balance. The energy demandhas to match the energy supply. In this figure, two level one controlleddistributed energy resources (CDER) DER 1 808 and DER 2 810 are shownbeing controlled by a Level 2 Power/Voltage controller 812. Thiscontroller supervises the two CDERs 808 and 810 to maintain an energybalance while disconnected and provide control of the total demand ofthe grid while the local EPS 802 is connected to the area EPS 800.

The demand setpoint is determined in two ways: if connected, the demandfrom the area EPS is determined such that the maximum value to the localEPS 802 is achieved; if disconnected, the supply and demand isdetermined by the available energy in the CDERs 808 and 810 and theproduction of power from uncontrolled DERs 814, 816, or loads 818.

PMUs are used for control of the CDERs 808 and 810 at high data rates,typically 60 Hz. The setpoints for the CDERs are determined by the level2 Power/Voltage controller 812. Note that the level 2 controller 812sends both real and reactive power commands to the CDERS 808 and 810 aswell as frequency and voltage setpoint commands. The real and reactivepower commands ensure an energy balance in the local EPS and thefrequency and voltage setpoints ensure that the voltage and voltageangle of the local EPS tracks the voltage and voltage angle of the areaEPS. This allows the local EPS 802 to disconnect and reconnect to thearea EPS 800 on command. This is an important feature of any microgridcontroller.

The invention claimed is:
 1. A method for decoupling control of real andreactive power of a local electrical power system having multipledistributed energy resources at non-co-located points, the methodcomprising: feeding back time-synchronized measurements of voltagephasors and current phasors from multiple phasor measurement units tomultivariable linear decoupling controllers; and controlling thedistributed energy resources by the multivariable linear decouplingcontrollers using linear control by sending, to the distributed energyresources, real and reactive power setpoint pairs derived from thetime-synchronized measurements of voltage phasors and current phasors.2. The method of claim 1, wherein the feeding back comprises feedingback phasor measurements from multiple level 1 controllers to a level 2controller, and wherein the multivariable linear decoupling controllersform a hierarchical feedback control system.
 3. The method of claim 1,wherein the feeding back comprises converting measured real and reactivepower values to current and power angle phasors.
 4. The method of claim1, wherein the feeding back comprises converting measured real andreactive power values to voltages and voltage angle differences betweenpoints of interest and the distributed energy resources.
 5. The methodof claim 1, wherein controlling the distributed energy resources by themultivariable linear decoupling controllers comprises using aproportional-integral controller combined with a derivative filter tomitigate power grid disturbances, and an output filter to adjust outputsetpoint pairs according to a response characteristic of the distributedenergy resources.
 6. The method of claim 1, wherein controlling thedistributed energy resources by the multivariable linear decouplingcontrollers comprises using an internal predictive model to account forsystem dynamics and transport delay in obtaining phasor feedback.
 7. Themethod of claim 1, wherein controlling the distributed energy resourcesby the multivariable linear decoupling controllers comprises using afeed forward filter for providing a faster phasor control in response toimmediate set point changes.
 8. The method of claim 1, whereincontrolling the distributed energy resources comprises computing thereal and reactive power setpoint pairs to achieve a predetermined powercontrol at a Point Of Interest.
 9. The method of claim 1, wherein themultiple distributed energy resources comprise a combination of energygeneration devices, controllable energy loads, and energy storagedevices.
 10. A system for decoupling control of real and reactive powerof a local electrical power system having multiple distributed energyresources at non-co-located points, the system comprising: one or morecontrollers; memory storing instructions which when executed by at leastone controller result in operations comprising: feeding backtime-synchronized measurements of voltage phasors and current phasorsfrom multiple phasor measurement units to multivariable lineardecoupling controllers; and controlling the distributed energy resourcesby the multivariable linear decoupling controllers using linear controlalgorithms by sending, to the distributed energy resources, real andreactive power setpoint pairs derived from the time-synchronizedmeasurements of voltage phasors and current phasors.
 11. The system ofclaim 10, wherein the feeding back comprises feeding back phasormeasurements from multiple level 1 controllers to a level 2 controller,and wherein the multivariable linear decoupling controllers form ahierarchical feedback control system.
 12. The system of claim 10,wherein the feeding back comprises converting measured real and reactivepower values to current and power angle phasors.
 13. The system of claim10, wherein the feeding back comprises converting measured real andreactive power values to voltages and voltage angle differences betweenpoints of interest and the distributed energy resources.
 14. The systemof claim 10, wherein controlling the distributed energy resources by themultivariable linear decoupling controllers comprises using aproportional-integral controller combined with a derivative filter tomitigate power grid disturbances, and an output filter to adjust outputsetpoint pairs according to a response characteristic of the distributedenergy resources.
 15. The system of claim 10, wherein controlling thedistributed energy resources by the multivariable linear decouplingcontrollers comprises using an internal predictive model to account forsystem dynamics and transport delay in obtaining phasor feedback. 16.The system of claim 10, wherein controlling the distributed energyresources by the multivariable linear decoupling controllers comprisesusing a feed forward filter for providing a faster phasor control inresponse to immediate set point changes.
 17. The system of claim 10,wherein controlling the distributed energy resources comprises computingthe real and reactive power setpoint pairs to achieve a predeterminedpower control at a Point Of Interest.
 18. The system of claim 10,wherein the multiple distributed energy resources comprise a combinationof energy generation devices, controllable energy loads, and energystorage devices.
 19. A controller having computer-readable programinstructions, which when executed result in operations comprising:feeding back time-synchronized measurements of voltage phasors andcurrent phasors from multiple phasor measurement units to multivariablelinear decoupling controllers; and controlling the distributed energyresources by the multivariable linear decoupling controllers usinglinear control algorithms by sending, to the distributed energyresources, real and reactive power setpoint pairs derived from thetime-synchronized measurements of voltage phasors and current phasors.20. The controller of claim 19, wherein the feeding back comprisesfeeding back phasor measurements from multiple level 1 controllers to alevel 2 controller, and wherein the multivariable linear decouplingcontrollers from a hierarchical feedback control system.
 21. Thecontroller of claim 19, wherein the feeding back comprises convertingmeasured real and reactive power values to current and power anglephasors.
 22. The controller of claim 19, wherein the feeding backcomprises converting measured real and reactive power values to voltagesand voltage angle differences between points of interest and thedistributed energy resources.
 23. The controller of claim 19, whereincontrolling the distributed energy resources by the multivariable lineardecoupling controllers comprises using a proportional-integralcontroller combined with a derivative filter to mitigate power griddisturbances, and an output filter to adjust output setpoint pairsaccording to a response characteristic of the distributed energyresources.
 24. The controller of claim 19, wherein controlling thedistributed energy resources by the multivariable linear decouplingcontrollers comprises using an internal predictive model to account forsystem dynamics and transport delay in obtaining phasor feedback. 25.The controller of claim 19, wherein controlling the distributed energyresources by the multivariable linear decoupling controllers comprisesusing a feed forward filter for providing a faster phasor control inresponse to immediate set point changes.
 26. The controller of claim 19,wherein controlling the distributed energy resources comprises computingthe real and reactive power setpoint pairs to achieve a predeterminedpower control at a Point Of Interest.
 27. The controller of claim 19,wherein the multiple distributed energy resources comprise a combinationof energy generation devices, controllable energy loads, and energystorage devices.